A stall-then-fall is a move where the character pauses a bit, then dives down.
Some stall-then-falls such as Toon Link's can be used to spike, while others like Mr. Game And Watch's do decent to good damage at once - and usually potent knockback, too. However, this is not to say it has no disadvantages - time it wrongly and you will be plunged down into the oblivion beyond the blast line. Be cautious if you want to use this move, or you can kiss your self-destruct-less streak goodbye.
Most stall-then-falls are with down aerials, but some are with down specials - namely Captain Falcon's, Ganondorf's, Bowser's, Kirby's (see left), and Yoshi's. Due to this "transition", their stall-then falls are quite unique. Bowser's and Yoshi's make them do a midair jump to the left right before their stall, Kirby's goes straight down, and Captain Falcon's and Ganondorf's have a different effect on the ground.
This type of move has a use besides dealing damage, though. For example, for characters such as Sonic, they will want to use a stall-then-fall to get back down after jumping a high distance. The thing is, this may pose a higher risk of self-destructing.
Stall-then-falls has it's ups and downs - try using it to its full potential.